# Whole number

Whole numbers are the set of positive integers; no fraction, decimal, or negative numeral can be a whole number. Whole numbers include 0 and all the cardinal numbers. In mathematical notation, we can specify the set of whole numbers as:

{0, 1, 2, 3, 4, 5, 6, ...}

Whole numbers can also be expressed using a number line:

Note that only the points on the number line that have labeled values are whole numbers. Depending on the definitions used, whole numbers may be synonymous with natural numbers.

## Natural numbers vs whole numbers

Two main definitions of natural numbers are used. One of the definitions is the set of numbers:

{0, 1, 2, 3, 4, 5, 6, ...}

In this case, the definition of natural numbers is identical to that of whole numbers.

The other commonly used definition of natural numbers is the set of numbers:

{1, 2, 3, 4, 5, 6, ...}

The only difference between this set and the one above is that it doesn't include zero. In this definition of natural numbers, whole numbers are used to indicate that 0 is included in the set of numbers.

## Whole number vs integer

Integers include negative values. Aside from this difference, the set of whole numbers and integers include the same values. This means that a whole number is always an integer, but an integer is not always a whole number.

The set of whole numbers: | {0, 1, 2, 3, 4, 5, 6, ...} |

The set of integers: | {..., -3, -2, -1, 0, 1, 2, 3, ...} |

If we took the absolute value of any integer, we would get a whole number.

## Is 0 a whole number?

Yes 0 is a whole number. This is simply by definition. It is included in the set of whole numbers as part of the definition.